Mathematics tests

Mark schemes forMental mathematicsTests A, B and C2005

3KEY STAGE

LOWER TIER &HIGHER TIERS

Ma20

05satspapers.org

First published in 2005

© Qualifications and Curriculum Authority 2005

Reproduction, storage, adaptation or translation, in any form or by any means, of this

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Produced in Great Britain by the Qualifications and Curriculum Authority under the authority

and superintendence of the Controller of Her Majesty’s Stationery Office and Queen’s Printer

of Acts of Parliament.

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Charities Act 1993.

Qualifications and Curriculum Authority

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W1J 8QA

www.qca.org.uk/

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33

Introduction

This booklet contains the mark schemes for the higher tiers tests (Tests A and B) and

the lower tier test (Test C). The pupil answer sheets will be marked by external

markers who will follow the mark schemes in this booklet, which are provided here for

teachers’ reference.

General guidance for markers

Please note that pupils should not be penalised if they record any information given in

the question or show their working. Ignore any annotation, even if in the answer

space, and mark only the answer. Accept an unambiguous answer written in the

stimulus box, or elsewhere on the page, but clearly attributable to the relevant

question.

General guidance for marking the written tests also applies to marking the mental

mathematics tests. In addition, please apply the following principles unless specific

instructions to the contrary are given in the mark scheme:

■ accept responses in words and/or figures,

eg 7 point 3, 4 hundred;

■ accept any unambiguous indication of the correct response from a given list,

eg circling, ticking, underlining;

■ accept unambiguous misspellings;

■ accept units that have been correctly converted to a different unit provided the new

unit is indicated. Where units have been given on the answer sheet, do not penalise

pupils for writing the units again;

■ accept responses with commas as spacers,

eg 50,000

but do not accept a point used as a spacer,

eg 50.000

satspapers.org

4

Low

er t

ier

Test

C q

ues

tio

ns

‘No

w w

e ar

e re

ady

to s

tart

th

e te

st.

‘Fo

r th

e fi

rst

gro

up

of

qu

esti

on

s yo

u w

ill h

ave

5 se

con

ds

to w

ork

ou

t ea

ch a

nsw

eran

d w

rite

it d

ow

n.’

1W

rite

in f

igu

res

the

nu

mb

er f

ive

hu

nd

red

an

d e

igh

t.

2W

hat

do

yo

u n

eed

to

ad

d t

o e

igh

ty-t

hre

e to

mak

e o

ne

hu

nd

red

?

3Lo

ok

at t

he

equ

atio

n o

n y

ou

r an

swer

sh

eet.

Wh

ena

equ

als

seve

n, w

hat

is t

he

valu

e o

f b?

4W

hat

nu

mb

er m

ult

iplie

d b

y ei

gh

t eq

ual

s fo

rty-

eig

ht?

5Lo

ok

at t

he

nu

mb

er o

n y

ou

r an

swer

sh

eet.

D

ivid

e it

by

on

e h

un

dre

d.

6W

hat

is t

he

sum

of

the

ang

les

in a

tri

ang

le?

7W

rite

th

e fr

acti

on

on

yo

ur

answ

er s

hee

t in

its

sim

ple

st f

orm

.

8Lo

ok

at t

he

exp

ress

ion

on

yo

ur

answ

er s

hee

t.W

rite

it a

s si

mp

ly a

s p

oss

ible

.

‘Fo

r th

e n

ext

gro

up

of

qu

esti

on

s yo

u w

ill h

ave

10 s

eco

nd

s to

wo

rk o

ut

each

an

swer

and

wri

te it

do

wn

.’

9I b

uy

a n

ote

bo

ok

for

fift

y p

ence

.H

ow

mu

ch c

han

ge

sho

uld

I g

et f

rom

a t

wo

po

un

d c

oin

?

10Lo

ok

at t

he

nu

mb

ers

on

yo

ur

answ

er s

hee

t.

Ad

d t

hem

.

11A

tra

in le

aves

at

ten

th

irty

am

an

d t

rave

ls f

or

fou

r h

ou

rs.

At

wh

at t

ime

do

es t

he

trai

n s

top

?W

rite

yo

ur

answ

er u

sin

g a

m o

r p

m.

12I a

m c

ou

nti

ng

bac

k in

ste

ps

of

ten

.O

ne

hu

nd

red

an

d t

wen

ty-f

ive,

on

e h

un

dre

d a

nd

fif

teen

, o

ne

hu

nd

red

an

d f

ive,

…W

rite

do

wn

th

e n

ext

nu

mb

er.

13W

hat

is h

alf

of

seve

n?

14Lo

ok

at t

he

tem

per

atu

res

on

yo

ur

answ

er s

hee

t.Pu

t a

rin

g r

ou

nd

th

e te

mp

erat

ure

th

at is

th

e lo

wes

t.

15Si

x h

un

dre

d p

eop

le w

ent

on

ho

liday

.Th

e p

ie c

har

t sh

ow

s h

ow

th

ey t

rave

lled

.H

ow

man

y p

eop

le t

rave

lled

by

car?

‘No

w t

urn

ove

r yo

ur

answ

er s

hee

t.’

Pra

cti

ce

qu

esti

on

Tim

e:

5 s

eco

nd

s

Tim

e:

10 s

eco

nd

s

90

11

22

33

b=

14 +

a

44

55

9300

77

3 9

88

3m

+m

99

£50

p

10

10

2528

11

11

10:3

0am

12

12

125,

115,

105,

13

13

14

14

–1°

C5°

C–

3°C

2°C

0°C

15

15

peo

ple

Pla

ne

Trai

nC

ar

Tim

e:

5 s

eco

nd

s c

on

tin

ue

d

66

°

Key s

tag

e 3

math

em

ati

cs 2

005

Men

tal

math

em

ati

cs

Test

C

Fir

st

na

me

Last

na

me

Sch

oo

l

To

tal

mark

s

Pup

il an

swer

sh

eet

satspapers.org

5

16W

rite

do

wn

an

eve

n n

um

ber

th

at is

a m

ult

iple

of

seve

n.

17Tw

o r

ule

rs c

ost

eig

hty

pen

ce.

Ho

w m

uch

do

th

ree

rule

rs c

ost

?

18H

ow

man

y se

con

ds

are

ther

e in

on

e an

d a

hal

f m

inu

tes?

19Th

ere

wer

e tw

o t

ho

usa

nd

peo

ple

at

a co

nce

rt.

Nin

e h

un

dre

d a

nd

nin

ety-

two

of

them

wer

e w

om

en.

Ho

w m

any

of

the

peo

ple

wer

e n

ot

wo

men

?

20Lo

ok

at t

he

nu

mb

ers

on

yo

ur

answ

er s

hee

t.W

ork

ou

t th

eir

ran

ge.

21Th

e te

mp

erat

ure

was

min

us

two

deg

rees

Cel

siu

s.A

t n

igh

t th

e te

mp

erat

ure

fel

l by

seve

n d

egre

es.

Wh

at w

as t

he

tem

per

atu

re a

t n

igh

t?

22Lo

ok

at t

he

shad

ed t

rian

gle

dra

wn

on

a c

enti

met

re s

qu

are

gri

d.

Wh

at is

th

e ar

ea o

f th

is t

rian

gle

?

23W

hat

is t

wen

ty p

er c

ent

of

sixt

y p

ou

nd

s?

24Lo

ok

at t

he

tria

ng

le o

n t

he

gri

d.

Wri

te t

he

coo

rdin

ates

of

the

po

int

mar

ked

A.

‘Fo

r th

e n

ext

gro

up

of

qu

esti

on

s yo

u w

ill h

ave

15 s

eco

nd

s to

wo

rk o

ut

each

an

swer

and

wri

te it

do

wn

.’

25Pe

op

le a

t a

sho

pp

ing

cen

tre

vote

d f

or

thei

r fa

vou

rite

fru

it d

rin

k.Th

e b

ar c

har

t sh

ow

s th

e re

sult

s.A

lto

get

her

, ho

w m

any

peo

ple

vo

ted

?

26I f

ace

wes

t, t

hen

I tu

rn t

hro

ug

h t

wo

rig

ht

ang

les.

Wh

at d

irec

tio

n a

m I

faci

ng

no

w?

27Lo

ok

at t

he

shap

e m

ade

fro

m s

mal

l eq

uila

tera

l tri

ang

les.

Shad

e tw

o m

ore

tri

ang

les

so t

hat

th

e sh

ape

has

th

ree

lines

of

sym

met

ry.

28I a

m t

hin

kin

g o

f tw

o n

um

ber

s th

at a

dd

to

ten

.Th

e tw

o n

um

ber

s m

ult

iply

to

get

her

to

mak

e tw

enty

-on

e.W

hat

are

my

two

nu

mb

ers?

29W

hic

h o

ne

of

the

shap

es o

n y

ou

r an

swer

sh

eet

is t

he

net

of

a cu

be?

Put

a ti

ck in

sid

e th

e co

rrec

t sh

ape.

30I h

ave

twen

ty-f

ive

card

s.Si

xtee

n o

f th

em s

ho

w e

ven

nu

mb

ers

and

th

e re

st s

ho

w o

dd

nu

mb

ers.

I am

go

ing

to

tak

e a

card

at

ran

do

m.

Wh

at is

th

e p

rob

abili

ty t

hat

th

e ca

rd w

ill s

ho

w a

n o

dd

nu

mb

er?

‘Pu

t yo

ur

pen

s d

ow

n.

The

test

is f

inis

hed

.’

Tim

e:

10 s

eco

nd

s c

on

tin

ue

dT

ime

:1

5 s

eco

nd

s

16

16

17

17

£80

p

18

18

seco

nd

s

19

19

2000

992

20

20

3,8,

3,1,

4

21

21

°C–

2°C

22

22cm

2

23

23

££

60

24

24

(,

)

4 2 0 –2 –4

0 2

4

A

BC

25

25

peo

ple

26

26

W

27

27

28

28

and

29

29

30

30

25 c

ard

s16

eve

n n

um

ber

s

satspapers.org

6

Time: 5 seconds

Time: 10 seconds

Time: 5 seconds continuedKey stage 3 mathematics 2005Mental mathematics lower tier Test C

Test CMark scheme

1 508 Do not accept responsesgiven in words

2 17 Accept embeddedvalue, eg 83 + 17

4 6 Accept embeddedvalue, eg 6 t 8

5 93

3 21

6 180 °

7 13

Do not accept equivalent fractions or decimals

11 2:30 pm Accept 14:30(pm)

Do not accept2:30 without pm

9 £ 1.50

10 53

12 95

133

12

Accept equivalent fractions or decimals

14

15 150 people

8 4m

satspapers.org

7

Time: 10 seconds continued Time: 15 seconds

16 Any number that is amultiple of 14,eg 14 or 700

Accept zero, and negative multiples of 14

17 £ 1.20

18 90 seconds

19 1008

21 –9 °C

20 7 Do not accept8 – 1

22 5 cm2

23 £ 12

24 ( 3 , – 2 )

25 27 people

26 East Accept any unambiguousindication of East,

eg E

27

29

28 3 and 7 Accept pair in either order

30 925

Accept equivalent probabilities

satspapers.org

8

Hig

her

tie

rs T

est

A q

ues

tio

ns

‘No

w w

e ar

e re

ady

to s

tart

th

e te

st.

‘Fo

r th

e fi

rst

gro

up

of

qu

esti

on

s yo

u w

ill h

ave

5 se

con

ds

to w

ork

ou

t ea

ch a

nsw

eran

d w

rite

it d

ow

n.’

1H

ow

man

y si

xes

are

ther

e in

fif

ty-f

ou

r?

2Lo

ok

at y

ou

r an

swer

sh

eet.

Wri

te t

he

coo

rdin

ates

of

the

po

int

mar

ked

A.

3Th

e p

op

ula

tio

n o

f Fr

ance

is a

pp

roxi

mat

ely

sixt

y-o

ne

mill

ion

. W

rite

th

is n

um

ber

in f

igu

res.

4H

ow

man

y m

illim

etre

s ar

e th

ere

in o

ne

met

re?

5W

rite

a d

iffe

ren

t fr

acti

on

th

at is

eq

uiv

alen

t to

th

ree-

fift

hs.

6W

hat

is s

ix p

oin

t tw

o m

ult

iplie

d b

y o

ne

tho

usa

nd

?

7Lo

ok

at t

he

dia

gra

m.

The

lines

mar

ked

wit

h a

rro

ws

are

par

alle

l.W

hat

is t

he

size

of

ang

le p

?

8R

ou

nd

th

ree

po

int

seve

n n

ine

five

to

on

e d

ecim

al p

lace

.

‘Fo

r th

e n

ext

gro

up

of

qu

esti

on

s yo

u w

ill h

ave

10 s

eco

nd

s to

wo

rk o

ut

each

an

swer

and

wri

te it

do

wn

.’

9Th

e sc

ale

on

a m

ap is

on

e ce

nti

met

re t

o f

ive

met

res.

On

th

e m

ap t

he

len

gth

of

a st

reet

is e

igh

t ce

nti

met

res.

Wh

at is

th

e re

al le

ng

th o

f th

e st

reet

in m

etre

s?

10W

rite

do

wn

a n

um

ber

th

at is

a m

ult

iple

of

thre

e an

d is

als

o a

mu

ltip

le o

f fi

ve.

11Tw

o o

f th

e an

gle

s in

a t

rian

gle

are

six

ty d

egre

es a

nd

sev

enty

deg

rees

.W

hat

is t

he

size

of

the

thir

d a

ng

le?

12I s

tart

at

seve

n a

nd

co

un

t d

ow

n in

eq

ual

ste

ps;

sev

en, f

ou

r, o

ne.

Wri

te d

ow

n t

he

nex

t tw

o n

um

ber

s.

13Lo

ok

at t

he

exp

ress

ion

on

yo

ur

answ

er s

hee

t.W

rite

it a

s si

mp

ly a

s p

oss

ible

.

14W

hat

is e

igh

teen

mu

ltip

lied

by

nin

e?

15Th

e p

erim

eter

of

a re

ctan

gle

is t

wen

ty c

enti

met

res.

Its

len

gth

is s

even

cen

tim

etre

s.W

hat

is t

he

wid

th o

f th

e re

ctan

gle

?

16Fi

ve p

er c

ent

of

a n

um

ber

is s

ixte

en.

Wh

at is

tw

enty

-fiv

e p

er c

ent

of

the

nu

mb

er?

17Lo

ok

at t

he

equ

atio

n o

n y

ou

r an

swer

sh

eet.

Wh

at is

th

e va

lue

of

a?

‘No

w t

urn

ove

r yo

ur

answ

er s

hee

t.’

Pra

cti

ce

qu

esti

on

Tim

e:

5 s

eco

nd

s

3812

Tim

e:

5 s

eco

nd

s c

on

tin

ue

d

14

14

189

2

2

(,

)

4 2 0 02

4

AB

C

44

mm

1m

7

7

°

100˚

p

88

3.79

5

Tim

e:

10 s

eco

nd

s

99

m1

cm :

5m

10

10

35

11

11

°6

0°7

0°

12

12

7,4,

1,,

13

13

6g

+4h

+3g

–2

h

15

15

cm20

cm7

cm

17

17

32 –

2a=

24

Key s

tag

e 3

math

em

ati

cs 2

005

Men

tal

math

em

ati

cs

Test

A

Fir

st

na

me

Last

na

me

Sch

oo

l

To

tal

mark

s

11

54

33

66

6.2

55

3 5

16

16

5%16

Pup

il an

swer

sh

eet

satspapers.org

9

18Es

tim

ate

the

valu

e o

f n

ine

po

int

two

mu

ltip

lied

by

two

po

int

nin

e.

19I d

rive

ten

kilo

met

res

in t

wel

ve m

inu

tes.

Wh

at is

my

aver

age

spee

d in

kilo

met

res

per

ho

ur?

20Lo

ok

at t

he

exp

ress

ion

on

yo

ur

answ

er s

hee

t.M

ult

iply

ou

t th

e b

rack

ets.

‘Fo

r th

e n

ext

gro

up

of

qu

esti

on

s yo

u w

ill h

ave

15 s

eco

nd

s to

wo

rk o

ut

each

an

swer

and

wri

te it

do

wn

.’

21Th

e p

icto

gra

m s

ho

ws

the

nu

mb

er o

f g

irls

an

d b

oys

in a

yo

uth

clu

b.

Ho

w m

any

mo

re g

irls

th

an b

oys

are

in t

he

you

th c

lub

?

22Th

e p

ie c

har

t sh

ow

s th

e co

lou

r o

f ca

rs in

a c

ar p

ark.

Ther

e w

ere

twel

ve b

lue

cars

.A

pp

roxi

mat

ely,

ho

w m

any

cars

wer

e th

ere

alto

get

her

?

23W

hen

aeq

ual

s m

inu

s th

ree

and

beq

ual

s m

inu

s se

ven

, w

hat

is t

he

valu

e o

f a

min

us

b?

24Th

e m

ean

of

thre

e n

um

ber

s is

six

. Tw

o o

f th

e n

um

ber

s ar

e fi

ve.

Wh

at is

th

e th

ird

nu

mb

er?

25A

cir

cle

has

a r

adiu

s o

f si

x ce

nti

met

res.

Giv

e an

ap

pro

xim

ate

valu

e fo

r th

e ci

rcu

mfe

ren

ce o

f th

e ci

rcle

.

26W

hat

is t

wo

-th

ird

s o

f th

ree-

qu

arte

rs o

f ei

gh

ty?

27Lo

ok

at t

he

freq

uen

cy t

able

sh

ow

ing

th

e n

um

ber

of

peo

ple

tra

velli

ng

in c

ars.

Alt

og

eth

er, h

ow

man

y p

eop

le w

ere

trav

ellin

g?

28A

rec

tan

gle

has

an

are

a o

f ei

gh

t sq

uar

e ce

nti

met

res.

Wh

at is

th

e ar

ea o

f a

rect

ang

le w

ith

sid

es t

hat

are

all

twic

e as

lon

g?

29Lo

ok

at t

he

gra

ph

s.Pu

t a

rin

g r

ou

nd

th

e g

rap

h t

hat

has

th

e eq

uat

ion

yeq

ual

sx

plu

s o

ne.

30Lo

ok

at t

he

nu

mb

ers

on

yo

ur

answ

er s

hee

t.W

rite

do

wn

th

e n

um

ber

th

at is

hal

fway

bet

wee

n t

hem

.

‘Pu

t yo

ur

pen

s d

ow

n.

The

test

is f

inis

hed

.’

Tim

e:

10 s

eco

nd

s c

on

tin

ue

dT

ime

:1

5 s

eco

nd

s c

on

tin

ue

d

19

19

km/h

10km

12 m

inu

tes

27

27

peo

ple

No

. of

peo

ple

12

34

Freq

uen

cy5

40

1

29

29

y

x

y

x

y

x

y

x

20

20

2a(a

+ 4

)

21

21

Gir

ls

Bo

ys

= 4

peo

ple

22

22

Bla

ckR

ed

Oth

erB

lue

23

23

a=

–3

b=

–7

a–

b

25

25

cm

6cm

26

26

803 4

2 3

28

28

cm2

8cm

2

Tim

e:

15 s

eco

nd

s

24

24

55

18

18

9.2

2.9

30

30

12 5

satspapers.org

10

Time: 5 seconds

Time: 5 seconds continued

Time: 10 seconds

Key stage 3 mathematics 2005Mental mathematics higher tiers Test A

Test AMark scheme

3 61 000 000 Do not accept responsesgiven in words

1 9 Accept embedded values,eg 9 t 6

2 ( 3 , 1 )

4 1000 mm Do not acceptamended units

5

Do not accept equivalent decimals

Any fraction equivalent to

(except ), eg , 3050

610

35

35

6 6200

7 80 °

8 3.8 Do not accept equivalentfractions or decimals

9 40 m

10

Accept zero, and negative multiples of 15

Any number that is amultiple of 15,eg 15, 30, 300

11 50 °

12 –2 and –5 Accept pairin either order

13 9g + 2h

14 162

15 3 cm

16 80 Do not acceptincorrect % signs

17 4 Accept embedded values,eg 32 – 2 t 4

satspapers.org

11

Time: 10 seconds continued Time: 15 seconds continued

Time: 15 seconds

18 26 answer 28

19 50 km/h

21 6

22 32 answer 40

23 4

24 8

25 36 cm answer 38 cm

26 40

27 17 people

28 32 cm2

29

30 710

Accept equivalentfractions or decimals

Do not accept incorrect notation,

eg 3.55

20 2a2 + 8a Do not accept equivalent expressionscontaining brackets,

eg 2(a2 + 4a)

satspapers.org

12

Hig

her

tie

rs T

est

B q

ues

tio

ns

‘No

w w

e ar

e re

ady

to s

tart

th

e te

st.

‘Fo

r th

e fi

rst

gro

up

of

qu

esti

on

s yo

u w

ill h

ave

5 se

con

ds

to w

ork

ou

t ea

ch a

nsw

eran

d w

rite

it d

ow

n.’

1W

hat

is f

ort

y-tw

o m

ult

iplie

d b

y te

n?

2Lo

ok

at t

he

nu

mb

ers

on

yo

ur

answ

er s

hee

t.W

rite

do

wn

th

e n

um

ber

th

at is

th

e m

od

e.

3H

ow

man

y ce

nti

met

res

are

ther

e in

th

ree-

qu

arte

rs o

f a

met

re?

4Lo

ok

at t

he

exp

ress

ion

on

yo

ur

answ

er s

hee

t.W

rite

it a

s si

mp

ly a

s p

oss

ible

.

5W

hat

nu

mb

er is

eig

ht

less

th

an m

inu

s fo

ur?

6W

rite

on

e an

d a

hal

f m

illio

n in

fig

ure

s.

7R

ou

nd

tw

o p

oin

t si

x n

ine

fou

r to

on

e d

ecim

al p

lace

.

8Th

e le

ng

th o

f a

pie

ce o

f st

rin

g is

fo

urt

een

cen

tim

etre

s to

th

e n

eare

st c

enti

met

re.

Wh

at is

th

e m

inim

um

len

gth

th

is p

iece

of

stri

ng

co

uld

be?

9W

hat

is t

he

gra

die

nt

of

the

line

wit

h e

qu

atio

n y

equ

als

two

xp

lus

thre

e?

‘Fo

r th

e n

ext

gro

up

of

qu

esti

on

s yo

u w

ill h

ave

10 s

eco

nd

s to

wo

rk o

ut

each

an

swer

and

wri

te it

do

wn

.’

10W

rite

do

wn

a f

acto

r o

f th

irty

-six

th

at is

gre

ater

th

an t

en a

nd

less

th

an t

wen

ty.

11A

tra

in jo

urn

ey b

egan

at

ten

th

irty

-fiv

e am

an

d e

nd

ed a

t el

even

fif

teen

am

.H

ow

lon

g w

as t

he

trai

n jo

urn

ey in

min

ute

s?

12D

rin

ks c

ost

tw

enty

-eig

ht

pen

ce e

ach

. W

hat

is t

he

gre

ates

t n

um

ber

of

thes

e d

rin

ks I

can

bu

y w

ith

on

e p

ou

nd

?

13Pu

t a

cro

ss o

n t

he

gri

d t

o s

ho

w t

he

po

int

wit

h c

oo

rdin

ates

min

us

two

, on

e.

14Th

e p

rob

abili

ty I

will

be

late

fo

r sc

ho

ol i

s o

ne-

twen

tiet

h.

Wh

at is

th

e p

rob

abili

ty t

hat

I w

ill n

ot

be

late

fo

r sc

ho

ol?

‘No

w t

urn

ove

r yo

ur

answ

er s

hee

t.’

Pra

cti

ce

qu

esti

on

Tim

e:

5 s

eco

nd

s

Tim

e:

5 s

eco

nd

s c

on

tin

ue

d

Tim

e:

10 s

eco

nd

s

3812

11

42

13

13

0–

1–

2–

31

23

3 2 1 0

–1

–2

–3

2

2

66

57

55

8

44

5a

+ 3

a

33

cm3 4

77

2.69

4

99

y=

2x

+ 3

88

cm14

cm

12

12

28p

£1

10

10

36

11

11

min

ute

s

10:3

5am

11:1

5am

14

14

1 205

5

–4

66

Key s

tag

e 3

math

em

ati

cs 2

005

Men

tal

math

em

ati

cs

Test

B

Fir

st

na

me

Last

na

me

Sch

oo

l

To

tal

mark

s

Pup

il an

swer

sh

eet

satspapers.org

13

15Lo

ok

at t

he

dia

gra

m o

n y

ou

r an

swer

sh

eet.

Wh

at is

th

e ar

ea o

f th

e re

ctan

gle

?

16H

ow

man

y th

ird

s ar

e th

ere

in t

wo

?

17Lo

ok

at t

he

trap

eziu

m.

An

gle

ais

on

e h

un

dre

d a

nd

ten

deg

rees

.W

hat

is t

he

size

of

ang

le b

?

18So

lve

the

equ

atio

n, t

plu

s th

ree-

fift

hs

equ

als

on

e.

19La

st m

on

th m

y te

lep

ho

ne

bill

was

th

irty

po

un

ds.

This

mo

nth

it is

tw

enty

per

cen

t m

ore

.H

ow

mu

ch is

th

is m

on

th’s

bill

?

20Lo

ok

at t

he

exp

ress

ion

on

yo

ur

answ

er s

hee

t.It

s va

lue

is e

igh

ty-t

wo

.W

rite

an

exp

ress

ion

usi

ng

aan

db

wit

h a

val

ue

of

fort

y-o

ne.

21W

hat

is t

hre

e-q

uar

ters

of

a h

alf?

22Yo

ur

answ

er s

hee

t sh

ow

s th

e nt

h t

erm

of

a se

qu

ence

.W

hat

is t

he

sixt

h t

erm

in t

his

seq

uen

ce?

23W

ork

ou

t th

e va

lue

of

two

to

th

e p

ow

er s

ix d

ivid

ed b

y tw

o s

qu

ared

.

‘Fo

r th

e n

ext

gro

up

of

qu

esti

on

s yo

u w

ill h

ave

15 s

eco

nd

s to

wo

rk o

ut

each

an

swer

and

wri

te it

do

wn

.’

24Lo

ok

at t

he

two

po

ints

on

th

e sq

uar

e g

rid

.Pu

t o

ne

mo

re c

ross

on

th

e g

rid

so

th

at t

he

thre

e p

oin

ts jo

in t

o f

orm

an

iso

scel

es t

rian

gle

.

25Lo

ok

at t

he

calc

ula

tio

n o

n y

ou

r an

swer

sh

eet.

Wri

te a

n a

pp

roxi

mat

e an

swer

.

26Te

n o

ut

of

thir

ty-s

ix p

eop

le s

aid

th

ey a

te t

oas

t fo

r b

reak

fast

.W

hat

an

gle

sh

ou

ld r

epre

sen

t th

is o

n a

pie

ch

art?

27Lo

ok

at t

he

circ

le w

ith

rad

ius

thre

e.O

ne

of

the

valu

es b

elo

w is

its

area

.Pu

t a

rin

g r

ou

nd

th

e co

rrec

t va

lue.

28Lo

ok

at t

he

nu

mb

ers

on

yo

ur

answ

er s

hee

t.Pu

t th

em in

ord

er o

f si

ze s

tart

ing

wit

h t

he

smal

lest

.

29W

rite

tw

o n

um

ber

s w

ith

a m

ean

of

six

and

a r

ang

e o

f fo

ur.

30A

cu

be

has

a v

olu

me

of

eig

ht

cub

ic c

enti

met

res.

Wh

at is

th

e vo

lum

e o

f a

cub

e w

ith

ed

ges

th

at a

re a

ll tw

ice

as lo

ng

?

‘Pu

t yo

ur

pen

s d

ow

n.

The

test

is f

inis

hed

.’

Tim

e:

10 s

eco

nd

s c

on

tin

ue

dT

ime

:1

5 s

eco

nd

s

26

26

°10 36

15

15

cm2

6cm

4cm

16

16

21 3

17

17

°

19

19

££

3020

%

18

18

t+

= 1

3 5

20

20

6a

+4

b82

21

21

1 23 4

22

22

n(n

+ 1

)1 2

23

23

26 22

24

24

25

25

523.

6+

27

27

3π

6π

9π

12π

15π

3

30

30

cm3

8cm

3

28

28,

,

0.4

25%

1 5

29

29

and

64

1.4

satspapers.org

14

Time: 5 seconds

Time: 5 seconds continued

Time: 10 seconds

Key stage 3 mathematics 2005Mental mathematics higher tiers Test B

Test BMark scheme

1 420

2 5

3 75 cm Do not accept amended units

4 8a

5 –12

6 1500 000 Do not accept responsesgiven in words

7 2.7 Do not accept equivalentfractions or decimals

8 13.5 cm Accept equivalentfractions or decimals

9 2 Accept21

10 12 or 18

11 40 minutes

12 3 Accept reference to the remainder,

even if incorrect, eg 3 rem 16

14 1920

Accept equivalent probabilities

13

Accept inaccurate indication, provided the pupil’s intention is clear

0–1–2–3 1 2 3

3

2

1

0

–1

–2

–3

satspapers.org

15

Time: 10 seconds continued Time: 15 seconds

18 25

Accept equivalentfractions or decimals

Accept embedded values,

eg + 35

25

15 24 cm2

17 70 °

16 6 Accept embedded values,

eg 63

20

Accept correct expressions equated to 41

3a + 2b or equivalentor

6a + 4b – 41

19 £ 36

21 38

Accept equivalent fractions, decimals

or percentages

22 21 Do not accept incomplete processing,

eg 3(6 + 1)

23 16 Do not accept incomplete processing,

eg 24

24

Accept inaccurate indication,provided the pupil’s intention is clear

Indicates a point on the line,excluding the circle,

or one of the points marked

25 10 answer 10.5

Do not accept incomplete processing,

eg 525

26 100 °

27

28 , 25%, 0.415

Accept any unambiguous indication

of the correct order,eg 0.2, 0.25, 0.4

29 4 and 8 Accept pairin either order

30 64 cm3

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